Mechanical Engineering

Both are not recommended for Mechanical Engineering, neither Narula Institute of Technology nor Techno India Salt Lake.
The good colleges that you can opt for Mechanical Engineering are- Institute of Engineering and Management, MCKV Institute of Engineering, and Meghanad Saha Institute of Technology.

https://www.shiksha.com/b-tech/resources/wbjee-college-predictor.
Check the college you can get with your rank for mechanical branch.
All the best.

https://www.shiksha.com/search/question/answered?q=upsee&fb=week
Check here out which colleges you will get with your rank all the best.

For admission you need to give entrance exams like JEE Mains or else directly by going to the private college and giving some entrance exam conducted by them.

Hey,
Duration of the diploma course after 12th science is two years. Candidates after completion of 12th can join the diploma course through lateral entry mode. Candidates are admitted directly to the second year of the three year diploma course. Admission to the lateral entry diploma is done on the basis of marks scored in the lateral entry examination.

Yes, it is possible apply for GATE and score good marks.

Admissions are purely done on the JEE Mains rank so I'd suggest you to visit josaa.nic.in and check the previous year's cutoffs of your home state NITs as in most of the cases it is easier to get home state NIT because of home state quota.

Yes u get detail call 09971067348.